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Discrete limit theorems for the Laplace transform of the Riemann zeta-function
Communications in Mathematics, Tome 13 (2005) no. 1, pp. 19-27 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In the paper discrete limit theorems in the sense of weak convergence of probability measures on the complex plane as well as in the space of analytic functions for the Laplace transform of the Riemann zeta-function are proved.
In the paper discrete limit theorems in the sense of weak convergence of probability measures on the complex plane as well as in the space of analytic functions for the Laplace transform of the Riemann zeta-function are proved.
Classification : 11M06, 44A10, 60F05
Keywords: Laplace transform; probability measure; Riemann zeta-function; weak convergence 
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Kačinskaitė, R.; Laurinčikas, A. Discrete limit theorems for the Laplace transform of the Riemann zeta-function. Communications in Mathematics, Tome 13 (2005) no. 1, pp. 19-27. http://geodesic.mathdoc.fr/item/COMIM_2005_13_1_a2/

[1] Atkinson F. V.: The mean value of the Riemann zeta-function. Acta Math., 81 (1949), 353–376. | DOI | MR | Zbl

[2] Billingsley P.: Convergence of Probability Measures. Wiley, New York, 1968. | MR | Zbl

[3] Conway J. B.: Functions of One Complex Variable. Springer-Verlag, New York, 1973. | MR | Zbl

[4] Heyer H.: Probability Measures on Locally Compact Groups. Springer-Verlag, Berlin, 1977. | MR | Zbl

[5] Ivič A.: The Riemann Zeta-Function. Wiley, New York, 1985. | MR

[6] Jutila M.: Atkinson’s formula revisited. in: Voronoi’s Impact in Modern Science, Book 1, Proc. Inst. Math. National Acad. Sc. Ukraine, Vol. 21, P. Engel and H. Syta (Eds), Inst. Math., Kyiv, 1998, pp. 137–154. | Zbl

[7] Laurinčikas A.: Limit theorems for the Laplace transform of the Riemann zeta-function. Integral Transf. Special Functions (to appear). | MR